标题： 渐近平直时空的$C^3$匹配 显示英文标题

标题： $C^3$ matching for asymptotically flat spacetimes

摘要： 我们提出了一种标准，用于寻找爱因斯坦方程的内部解与外部渐近平直解能够匹配的最小距离。 该标准基于黎曼曲率张量及其一阶导数的特征值分析，隐含了$C^3$个可微性条件。 匹配本身通过要求曲率特征值在匹配面的连续性来实现。 我们将$C^3$匹配方法应用于球对称完美流体时空，并得到了密度和压强在匹配面上应为零这一具有物理意义的条件。 测试了几种牛顿引力和爱因斯坦引力下的完美流体解。 显示英文摘要

摘要： We propose a criterion for finding the minimum distance at which an interior solution of Einstein's equations can be matched with an exterior asymptotically flat solution. It is based upon the analysis of the eigenvalues of the Riemann curvature tensor and their first derivatives, implying $C^3$ differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the $C^3$ matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.